“I kind of kept the title in my back pocket for a long time,” Eleanor Friedberger says of her second solo album, Personal Record. The title is a joke that’s very much in line with the sly, elegant conceptual gestures she’s been pulling off for more than a decade. Personal Record’s songs are built around her voice and guitar playing, and its lyrics are in a confessional first-person mode, the kind that tends to be associated with a songwriter who used to be part of a group and has gone solo to make a “more personal record.”

That’s exactly what Friedberger’s done — from 2000 to 2011, she was the frontwoman of the Fiery Furnaces, the brainy, arty rock band, now on hiatus, that she formed with her brother Matthew. But the cover art of Personal Record suggests another meaning: It’s a photograph by her friend Moses Berkson, a long shot of Friedberger reaching the edge of a swimming pool. “I wanted to do something that was relatively glamorous without being overtly sexy,” she says. “It’s like a bikini shot, but it’s pretty obscured.”

And, in fact, Friedberger’s new songwriting mode was a very deliberate decision, she notes. “After Last Summer came out, I thought: I’m trying to be this other type of performer now, a singer-songwriter. What kind of songs does somebody like that write, and how am I going to put these songs across?” So the “You’re So Vain”-style blind items in songs like “When I Knew” and “Other Boys” (which mentions “the blonde who’s in a band with her twin” and “that sometime star of stage and screen/who had a bit part in a film back in her teens”) might be genuine revelations, or might be entirely fictional.

“That’s the secret!” Friedberger laughs. “That’s the mystery! I mean, I wrote the songs with somebody else [novelist/musician Wesley Stace]–how personal could it be? We wrote the words together, back and forth through the mail, and I set them to music. It was texts that could stand alone on a page, with or without music; that was the idea.”

The sound of Personal Record echoes the singer-songwriters of the past, especially the U.K. and California scenes of the early ’70s. “Of course, I’m taking cues from a lot of people–that’s the way I’ve always worked,” Friedberger says. “I thought I wanted the drums on ‘Other Boys’ to sound like Yoko Ono’s ‘Born in a Prison.’ Nobody else would recognize that–it doesn’t sound anything like that — but in my mind, that’s what I was going for. And now I’ve been listening to this one guy nonstop, a Nigerian singer, William Onyeabor. I can’t imagine that’s not going to influence my next record, but it’s the same thing: I don’t know if anyone’s going to be able to tell.”

Friedberger’s been playing in the U.S. with the group that recorded Personal Record, but she also just returned from a European tour on which she was backed by a different band (led by David Brewis of Field Music), and she’ll be playing solo as the opening act for Colin Meloy’s tour in November. At the Station to Station tour’s Kansas City pop-up show, she played a few songs with an ad hoc group including bassist Tim Koh of Ariel Pink’s Haunted Graffiti and champion whip-cracker Chris Camp.

That means that even these “personal” songs are constantly mutating on stage, which is the way Friedberger likes it. “The Fiery Furnaces,” she says, “never tried to recreate an album live–that was out of necessity, but also trying to set ourselves apart from everybody else. I think it’s a shame when you go to hear a band and they just play their album like you could hear it at home. That’s never made any sense to me. And I’m just not precious about the songs. That’s the fun part about performing: you can make up a new melody as you’re singing. Where else do you get the chance to do something like that?”